The solution to the first equation 4x – 5 = 16 is x = 5.25. The solution to the second equation 35 + 3x – 11 = 23 is x = -0.33. Both solutions have been rounded to two decimal places.
Explanation:Let's solve these two equations one by one:
a. 4x – 5 = 16
Add 5 to both sides of the equation: 4x = 16 + 5 Simplify right side: 4x = 21 Divide both sides by 4 to solve for x: x = 21/4 = 5.25
b. 35 + 3x – 11 = 23
Simplify the left side by combining like terms: 3x + 24 = 23 Subtract 24 from both sides to isolate the term with x: 3x = 23 - 24 Simplify right side: 3x = -1 Divide both sides by 3 to solve for x: x = -1/3 = -0.33
These are the solutions to the equations, rounded to two decimal places.
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F the measures, in degrees, of the three angles of a triangle are x,x+10, and 2x-6 the triangle must be
Answer: The triangle mentioned here is an acute angled triangle.
Step-by-step explanation: x+x+10+2x-6=180°(angle sum prop. of triangles)
= 4x+4=180°
= 4x=174°
= x=44°
therefore, x=44°
,x+10=44+10=54°
,2x-6=2(44)-6=82°
Write the equation of a line that passes through the points (0, -2) and (4, -5). Answer MUST be in standard form: Ax + By = C.
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b).
We have the points (4, -5) and (0, -2) → y-intercept → b = -2.
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Substitute:
[tex]m=\dfrac{-2-(-5)}{0-4}=\dfrac{-2+5}{-4}=\dfrac{3}{-4}=-\dfrac{3}{4}[/tex]
Therefore we have the equation of a line
[tex]y=-\dfrac{3}{4}x-2[/tex]
Convert to the standard form: [tex]Ax+By=C[/tex]
[tex]y=-\dfrac{3}{4}x-2\qquad\text{multiply both sides by 4}\\\\4y=-3x-8\qquad\text{add 3x to both sides}\\\\\boxed{3x+4y=-8}[/tex]
So for this, I will be putting the equation into slope-intercept form then rearranging it into standard form. Firstly, we need to solve for the slope. To do this, take the 2 coordinates given to us and solve as such:
[tex]\frac{-5-(-2)}{4-0}=-\frac{3}{4}[/tex]
Now, one of the coordinates given to us is (0,-2), which is the y-intercept. With all this info, our slope-intercept equation is [tex]y=-\frac{3}{4}x-2[/tex] . From here we can solve for the standard form.
Firstly, add 3/4x onto both sides of the equation:
[tex]\frac{3}{4}x+y=-2[/tex]
Now, it may appear that we are finished. However, 3/4 is not an integer (Integers are whole numbers). To make it an integer, we need to multiply both sides by 4:
[tex]3x+4y=-8[/tex]
Answer:In short, the standard form of this equation is 3x + 4y = -8.
What value of b will make the point (4,-3) lie on the line y=bx-2 in the standard (x,y) coordinate plane?
Plug the coordinates of the point in the equation and solve for b:
[tex] y=bx-2 \iff -3=4b-2 \iff 4b=-1 \iff b=-\dfrac{1}{4} [/tex]
There is a line whose slope is 0 and whose y -intercept is 9. What is its equation in slope-intercept form?
Answer:
y = 0x + 9
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
here m = 0 and c = 9, hence
y = 0x + 9
The equation of a horizontal line is normally written as y = 9
with the x- term omitted
The equation of a line with a slope of 0 and a y-intercept of 9 is y = 9, which represents a horizontal line on the graph.
The student is asking about the equation of a line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Given that the slope (m) is 0, and the y-intercept (b) is 9, the equation of the line is simply y = 0x + 9. Since any number multiplied by zero is zero, this simplifies to y = 9.
Therefore, the equation of the line with a slope of 0 and a y-intercept of 9 in slope-intercept form is y = 9. This represents a horizontal line that crosses the y-axis at 9.
A student has 20 pencils at the beginning of the school year. After a week, the student has 18 pencils left. If the student continues to use pencils at the same rate, which equation will represent pencils left after w weeks?
Answer: p = -2w + 20
Step-by-step explanation:
If the student had 20 pencils but now has 18 pencils, he uses pencils at a rate of 2 per week. So, m = -2 (negative because he is decreasing the amount of pencils). The student started with 20 pencils so b = 20
Use the y = mx + b but replace "y" with "p" and replace "x" with "w" and input the m and b as stated above:
p = -2w + 20
Zoe rounded 6 * 8493 to 6 * 8000. Andrew rounded 6 * 8493 + 6 * 9000 who will have an estimate closer to the actual product? How do you know? Explain another way to estimate 6 * 8493 that would give a better estimate
Answer: Zoe is closer to the actual product because 6.80 is closer to 6.8493 than 6.90 mathematically. Another way to estimate 6.8493 is to round to the nearest hundredth place: 6.85
Zoe will have an estimate closer to the actual product.
Explanation:To determine who will have an estimate closer to the actual product, we can compare the rounding methods used by Zoe and Andrew. Zoe rounded 6 * 8493 to 6 * 8000, while Andrew rounded 6 * 8493 + 6 * 9000. In this case, Andrew's estimate will be closer to the actual product because he considered additional terms in his calculation.
Another way to estimate 6 * 8493 that would give a better estimate is to round each term separately before multiplying. For example, rounding 6 to 10 and 8493 to 8500, the estimate would be 10 * 8500 = 85,000.
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The cost of a taxi ride is equal to $3.50 plus $0.25 for each mile. If a ride costs a total of $6.75 how long was the ride?
Answer:
13 miles
Step-by-step explanation:
Write and solve an equation involving this information, using x as the distance traveled, in miles:
Cost(x) = $6.75 = $3.50 + ($0.25/mile)x
First, subtract $3.50 from both sides, obtaining: $3.25 = ($.25/mile)x.
Next, divide both sides by $0.25/mile:
$3.25
x = ------------------ = 13 miles
$0.25/mile
The length of the taxi ride was 13 miles.
At a basketball game, a vender sold a combined total of 223 sodas and hot dogs. The number of hot dogs sold was 57 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold.
Answer: 140 Hot dogs and 83 sodas.
Step-by-step explanation:
Alright, so we will say that h = hot dogs and s = sodas.
h + s = 223
I have used the guess and test strategy to get:
h = 140
140 - 57 = 83
s = 83
Check: 83 + 140 = 223
Use the function below to answer the question.
[tex]f(x)=x^3+7x^2+16x+12=(x+2)(x+2)(x+3)[/tex]
What is the multiplicity of the root -3 ?
Answer:
1
Step-by-step explanation:
(x +3) appears only once as a factor, hence the multiplicity of the root x=-3 is 1.
PLZ HELP!! The question is attached!
Answer:
Step-by-step explanation:
Subtract the 680 from 960, then divide the product by 52000 to get the answer
the volume of this rectangular prism is 5x^3. what does the coefficient 5 mean in terms of the problem?
Answer:
the length is 5 times the width of the prism
Step-by-step explanation:
the volume of this rectangular prism is [tex]5x^3[/tex]
volume of the prism = length * width * height
Length of the prism = 5x
Width = x
height =x
Length of the prism = 5x = 5* width of the prism
So, the length is 5 times the width of the prism
What is the graph of the function f(x) = the quantity of x squared plus 3 x minus 4, all over x plus 4?
Answer:
Given the function:
f(x) = the quantity of x squared plus 3x minus 4 , all over x plus 4
i,e
[tex]f(x) = \frac{x^2+3x-4}{x+4}[/tex]
or
[tex]f(x) = \frac{x^2+4x-x-4}{x+4}[/tex]
or
[tex]f(x) = \frac{x(x+4)-1(x+4)}{x+4}[/tex]
or
[tex]f(x) = \frac{(x+4)(x-1)}{x+4}[/tex]
⇒y= f(x) = x -1 ......[1]
Find the x-intercepts and y-intercepts for the equation [1] ;
y-intercepts defined as the graph crosses the y-axis;
substitute x =0 to solve for y;
y = 0-1 = -1
y = -1
x-intercepts defined as the graph crosses the x-axis;
substitute y =0 to solve for x;
0 = x-1
or
x = 1
Plot these points (0 , -1) and (1, 0) on the graph for the given function as shown below.
Caiden earned $475 from mowing lawns last summer. He deposited this money in an account that pays an interest rate of 3.8% compounded annually. What will be his balance after 15 year?
Answer:
The balance after 15 year is $831.25 .
Step-by-step explanation:
Formula
[tex]Amount = P (1 + r)^{t}[/tex]
Where P is the principle and r is the rate of interest in the decimal form and t is the time.
As given
Caiden earned $475 from mowing lawns last summer.
He deposited this money in an account that pays an interest rate of 3.8% compounded annually.
Here
P = $475
3.8% is written in the decimal form.
[tex]= \frac{3.8}{100}[/tex]
= 0.038
r = 0.038
t = 15 years
Put in the formula
[tex]Amount = 475 (1 + 0.038)^{15}[/tex]
[tex]Amount = 475 (1.038)^{15}[/tex]
[tex]Amount = 475\times 1.75(Approx)[/tex]
Amount = $831.25
Therefore the balance after 15 year is $831.25 .
Caiden will have approximately $850.91 in his account after 15 years of interest compounded annually at a rate of 3.8%.
Explanation:In this problem, we're dealing with compound interest, not simple interest. The formula to calculate compound interest is: A = P (1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest; P is the principal amount (the initial money); r is the annual interest rate (in decimal); n is the number of times that interest is compounded per year; and t is the time the money is invested for in years. In this case, P equals $475, r equals 3.8/100 or 0.038 (transforming percentage to decimal), n is 1 (because the interest is compounded annually), and t is 15 years. Substituting these values into the formula gives: A = $475 (1 + 0.038/1)^(1*15). Calculate the bracketed part first, resulting in a figure around 1.038 and raise it to the power of 15, so we get a value around 1.7914. Multiply this by the initial amount of $475 to get the final balance after 15 years which will be approximately $850.91. Hence, Caiden will have $850.91 in his account after 15 years.
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A survey found that 12 out of every 15 people in the United States prefer eating at a restaurant over cooking at home. If 400 people selected eating at a restaurant on the survey, ow many people took the survey?
Answer:
It is 80
Step-by-step explanation:
This because of when we divided the number 400 by 15 we got 26.6' an infinite number this is how many times the survey 12/15 was taken then if we then times this by 3 we get 80 which is the amount of people who prefer their own dinner
A wildlife preservation group records the number of squirrels in a city park. The first count recorded is 30 squirrels. A second count of 60 squirrels is recorded six months later, and 120 squirrels are counted at the end of one year. Assuming that no squirrel dies and the growth rate remains the same, which function represents the number of squirrels after x years? A) f(x) = 30x B) f(x) = 302x C) f(x) = 30(2)x D) f(x) = 30(2)2x
Answer:
A F(x)=30x
Step-by-step explanation:
just plug number in to the equations to see which one matches
Answer: [tex]f(x)=30\cdot2^{2x}[/tex]
Step-by-step explanation:
Given: A wildlife preservation group records the number of squirrels in a city park.
The first count recorded = 30 squirrels.
A second count of 60 squirrels is recorded six months later, and 120 squirrels are counted at the end of one year.
The growth rate of squirrel=[tex]\frac{120}{30}=4=2^2[/tex]
The exponential growth equation is given by :-
[tex]y=Ab^n[/tex], where A is the initial amount , b is the growth rate and n is the time period.
If the growth rate remains constant, then the function represents the number of squirrels after x years is given by :-
[tex]f(x)=30\cdot(2^2)^x=30\cdot2^{2x}[/tex]
The following is an example of a convex polygon
True
False
Find the distance between points M(-1,-10) and P(-12,-3) Round to the nearest tenth
Answer:
13.0 units
Step-by-step explanation:
To find the distance between two points, we use the formula
d = sqrt( (y2-y1)^2+ (x2-x1)^2)
sqrt((-3--10)^2 + (-12--1)^2)
sqrt( (-3+10)^2 + (-12+1)^2)
sqrt( (7^2 + (-11)^2)
sqrt( 49+121)
sqrt( 170)
13.038
Rounding to the nearest tenth
13.0
Select the correct graph for the system of inequalities from the list of graphs. Indicate which graph represents the system, and list three possible solutions in the form of (x, y).
y greater or equal than minus 5 x plus 1 y greater than minus 4 x minus 2 y greater or equal than minus 2
Choose a graph from the list of graph, like in the picture.
A pitcher of fruit punch holds 2 gallons. If 9 people share the entire pitcher equally, how much punch will each person get?
Answer:
2/9
Step-by-step explanation:
2÷9=2/9A clerk is marking up merchandise 34% the original price of an item is 455 what will be the retail price
The length of a rectangular is 5 centimeters less then it width. The perimeter of the rectangle is 26
Answer: length = 7 c, and width = 6 cm
Step-by-step explanation:
A number has the digits 1, 9 and 5 to the nearest 100 the number rounds to 600. What is the number?
Answer:
591
Step-by-step explanation:
the closest number to 600 out of every combo
195
159
951
915
519
591
Answer: 591
Step-by-step explanation:
From the digit 1, 9 and 5. The following numbers can be gotten if we use the 3 numbers.
159
195
519
591
915
951
Of all the numbers, the closest to 600 are 519 and 591.
To the nearest 100, 519 gives 500 while 591 gives 600. Therefore, the answer is 591.
For a school drama performance, student tickets cost $5 each and adult tickets cost $10 each. The sellers collected $3,570 from 512 tickets sold. If c is the number of student tickets sold, which equation can be used to find the amount of tickets sold of each type?
10(512 – c) + 5c = 512
10(512 – c) + 5c = 3,570
5(512 – c) + 10c = 3,570
5(512 – c) + 10c 512
Answer: [tex]10(512 – c) + 5c = 3,570[/tex]
Step-by-step explanation:
Given : The number of student tickets sold is represented by c.
For a school drama performance, student tickets cost $5 each and adult tickets cost $10 each.
The sellers collected $3,570 from 512 tickets sold.
Since , the total tickets sold = 512
Therefore , the number of adults ticket = [tex]512-c[/tex]
Now, cost of total child tickets : [tex]5c[/tex]
Cost of total adult tickets = [tex]10(512 – c)[/tex]
Now, according to the cost of the tickets , we have the following equation :-
[tex]10(512 – c) + 5c = 3,570[/tex]
Find the slope-intercept form of the line passing through the point (7,-2) and parallel to the line y=-8x-4.
The slope-intercept form of the line passing through the point (7, -2) and parallel to the line y = -8x - 4 is y = -8x + 54. The required answer is y = -8x + 54.
To find the slope-intercept form of a line parallel to the given line, we need to determine the slope of the given line first.
The given line has a slope of -8 since it is in the form y = mx + b, where m represents the slope.
Since the line we are looking for is parallel to the given line, it will have the same slope of -8.
Now, we can use the point-slope form of a linear equation to find the equation of the line passing through the point (7, -2) with a slope of -8:
y - y1 = m(x - x1)
Substituting the values of the point and slope:
y - (-2) = -8(x - 7)
Simplifying:
y + 2 = -8x + 56
Rearranging the equation to the slope-intercept form:
y = -8x + 54
Therefore, the slope-intercept form of the line passing through the point (7, -2) and parallel to the line y = -8x - 4 is y = -8x + 54. The required answer is y = -8x + 54.
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Trey drives an average of 36 miles per day. How many days will it take him to drive 3,240 miles?
Answer:
90 days
Step-by-step explanation:
That = 3240 / 36
= 90 days
Answer:
90 days
Step-by-step explanation:
Hello, I think I can help you with this
You can easily solve this by using a simple rule of three.
Step one
Define
if the drives an average 36 miles per day,the how many days(x) will it take to drive 3240 miles :it is
1 day ⇔ 36 miles
x days ⇔ 3240 miles
the relation is
[tex]\frac{1\ day}{36\ miles}=\frac{x\ day}{3240\ miles}\\[/tex]
Step two
solve for x
[tex]\frac{1\ day}{36\ miles}=\frac{x\ day}{3240\ miles}\\\\x=\frac{1\ day*3240\ miles}{36\ miles}\\x=90\ days\\[/tex]
90 days
Have a great day.
Oceanside Bike Rental Shop charges 17 dollars plus 6 dollars an hour for renting a bike. Mike paid 71 dollars to rent a
bike. How many hours, h, did he pay to have the bike checked out? Write an equation and solve for h. Must show
your work to receive full credit.
Please show your work. Thank You.
Answer:
9 hours
Step-by-step explanation:
First off we need to subtract 17 from 71 in order to get rid of the initial cost. This will lead us to 54. The last thing we need to do is divide that by 6 since you pay 6 hours per hour. Mike paid 71 dollars to rent a bike for 9 hours.
A right triangle has legs that measure 7 cm and 6 cm. What is the length of the hypotenuse in meters?
Answer:
[tex]\sqrt{85} or 9.22[/tex]
Step-by-step explanation:
You need to remember the following equation:
[tex]a^{2} + b^{2} = c^{2}[/tex]
Where a and b is the lengths of the two sides and c is the hypotenuse.
So simply plug these values into this:
[tex]6^{2} + 7^{2} = h^{2}[/tex]
36 + 49 = h^2
36 + 49 = 85
So the hypotenuse is the square root of 85:
[tex]\sqrt{85} = 9.22[/tex]
The probability that a student at certain high school likes art is 36%. The probability that a student who likes art also likes science is 21%. Find the probability that a student chosen at random likes science given that he or she likes art. Round to the nearest tenth of a percent.
Answer: Probability that a student chosen at random likes science given that he or she likes art is 58%
Step-by-step explanation:
Since we have given that
Probability that a student who likes art and science = 21%
Probability that a student who likes art = 36%
According to question,
we need to find the probability that a student chosen at random likes science given that he or she likes art.
So, we will use "Conditional Probability":
P(A) = 0.36
P(S ∩ A) = 0.21
[tex]P(S\mid A)=\frac{P(S\cap A)}{P(A)}\\\\P(S\mid A)=\frac{0.21}{0.36}\\\\P(S\mid A)=0.58\\\\P(S\mid A)=58\%[/tex]
Hence, Probability that a student chosen at random likes science given that he or she likes art is 58%.
Claudia works as a manufacturer of decorative jewelry boxes. A customer would like her to create some boxes with the following conditions:
The sum of the length and width must be 30 centimeters.
The height must be 3 centimeters less than the length.
The box should have the greatest possible volume.
Let's do some math to see if we can decide what size boxes Claudia needs to make, and show what we know about polynomials in the process. Remember: One formula we can use to find the volume of a box is Length * Width * Height.
Answer:
l = 20.5 cm
h = 17.5 cm
w = 9.5 cm
Step-by-step explanation:
Conditions
l+w =30 Solving for w 30 - l = w
h = l-3
V = l*w*h
Substituting in
V = l * (30-l) * (l-3)
= (30l-l^2) (l-3)
= 30 l^2 - l^3 - 90l + 3l^2
Combining like terms
Step-by-step solution
-l^3 + 33 l^2 - 90 l
To find the maximum we need to take the first derivative and then set it equal to zero
-3l^2 + 66l -90 = 0
Factor out a -3
-3 (l^2 -22l +30) =0
Using my calculator and the quadratic formula
l = 11 - sqrt(91)
l = 11 + sqrt(91)
l = 1.5 or 20.5 approximately
If l = 1. then
h= l-3 would be negative so
l = 20.5
h = l-3
h = 17.5 approximately
w = 30-l = 9.5 approximately
A real estate aqent earns a commission on a house she sells. Her first commission is 5% on the first 500,000 of the sale price of the house. She then earns a 6% comission for the amount sbove 500,000 of the sale price of the house. How much commission did the agent earn if she sold the house for 585,000?